Question

Tickets sales to the local gaming convention, PlayerCon, are on the rise! Sales of 2-day tickets brought in $188,100. A total of 6,600 tickets were sold. Adult 2-day tickets cost $36.00 and children’s 2-day tickets cost $26.00. How many of each kind of ticket were sold?

Answer 1

• 1650 Adult tickets
• 4950 children's tickets

Explanation:

Using numerical reasoning

Sale of 6600 children's tickets would provide revenue of ...

... 6600×$26 = $171,600

Revenue was actually $188,100 -171,600 = $16,500 more than that. Each adult ticket sold instead of a children's ticket increases revenue by $36 -26 = $10, so there were $16,500/$10 = 1650 adult ticket sold.

The number of children's tickets was then 6600 -1650 = 4950.

_____

Using an equation

Let "a" represent the number of adult tickets sold. Then the number of children's tickets is (6600-a) and the total revenue is ...

... 36a +26(6600 -a) = 188,100

... 10a = (188,100 -171,600) . . . . . . . collect terms, subtract 26·6600

... 16,500/10 = a = 1650 . . . . . . . . . divide by the coefficient of "a"

... (6600 -a) = 6600 -1650 = 4950 . . . . . childrens's tickets sold.

There were 1650 adult and 4950 children's tickets sold.